Worksheet for calculating Day-of-Week (DOW) and the Month, Day or Year
(If you are calculating Day, Month, Year (or Century), use 0 for those variables in Steps 1-3.)
| Target Date: | Month | Day | Century | Year | = Day of Week |
| | | | | | |
| STEP 1 | | | |
| M | | | Value for the Month from the Month Table |
| D | | | Day |
| MD | + | | Add M and D |
| 7X | + | | The largest multiple of 7 contained in MD (i.e., 0,7,14,21,28,35) |
| MD’ | = | | Subtract 7X from MD 1/ and hold this number till Step 3. |
| | | | |
| STEP 2 | | | |
| Y | | | Last two digits of the year. |
| 28X | | | The largest multiple of 28 contained in Y2/ (i.e., 0, 28, 56 or 84) |
| Y’ | + | | Subtract 28X from YY1/ |
| L | + | | Divide Y’ by 4 (=____.___) and round result down (i.e., drop decimal)3/ |
| C | + | | Value for the century from the Century Table |
| adjustment | - | | Subtract 1 to adjust if date is Jan/Feb in leap year (no decimal in Y’/4)4/ |
| CY | = | | Add YY’+LY+C and subtract 1 as adjustment if appropriate5/ |
| | | | |
| STEP 3 | | | |
| MD’ | + | | MD’ from Step 1 |
| CY | + | | CY from Step 2 |
| Result | = | | Add MD’ plus CY |
| 7X | - | | The largest multiple of 7 contained in Result (i.e., 0,7,14,21,28, etc.) |
| Result’ | = | | Subtract 7X from Result’. This is the value for DOW if you are looking for the Day-of Week (see DOW Table). If you are looking for the Month, Day or Year, continue to Step 4 with this figure. |
| | | | |
| STEP 4 | | | This step is only for calculating the Month, Day, Year or Century |
| Result’ | | | Result’ from Step 3 above. |
| W | + | | Look up known Day of Week for target Date in DOW Table |
| adjustment | + | | Enter 7 here if Result is GREATER than W, otherwise enter 0. |
| W’ | = | | Add W plus any adjustment by 7 you made above |
| Target Value | | | Subtract Result’ from W’. This is the Target Value you are trying to find. (Note: if you are looking for the DAY and the Target Value is 0, since there is no 0 Day of the month, make it 7. |
| | | | |
| | | | If Target is DAY, Target Value is first occurrence that month; add 7, 14, 21 and 28 for second, third fourth and fifth occurrences. |
| | | If Target is MONTH, look up one or more months in Month Table with that value (remember to adjust for Jan and Feb in Leap Years: Jan =6 and Feb = 2) | |
| | | If Target is YEAR, start at one year and go forward one year at a time, calculating the CY (full year) value for each as you go along, until you find the first or additional matches with Target Value. If the Date is in Jan. or Feb, don’t forget to subtract one for full year values in leap years | |
| | | | If Target is CENTURY, look up Target Value in Century Table. |
Footnotes | ||
1 - The only reason you do this here is to make it simpler to remember the number if it is between 0 and 6 and not as computed initially. Otherwise, it will be done in Step 3. | ||
2 - Why 28? Because there are 7 days in a week and 4 years in a leap year cycle the calendar cycle within a century repeats itself every 28 years (but not for Jan/Feb of ’00 years not evenly divisible by 400). | ||
3- This step is to adjust for leap years. But it adds in the extra day for a full leap year. | ||
4 - Turn-of-century (i.e., ’00) years are not leap years unless they are evenly divisible by 400. | ||
5 - You could reduce this CY figure by the largest multiple of 7 contained in it to get a true CY between 0 and 6, but there is no need at this point since you will do it soon in step 3. HERE IS THE JPEG IMAGE FOR THE WORKSHEET  | ||
